The publication “Nanoscale Electrostatic Manipulation of Magnetic Flux Quanta in Ferroelectric/superconductor BiFeO3/YBaCu3O7 Heterostructures” by Crassous et al. Physical Review Letters, 107, 247000 (2011) demonstrates the feasibility of doping a superconductive material of hybrid structure comprising a stack of two layers: a first layer of a superconductive material and a second layer of a ferroelectric material.
The principle of this doping lies in the creation of an electric field in the ferroelectric second material. The ferroelectric second material is polarized or possesses a component of its polarization in a direction parallel to the direction of the stack. The orientation of the electric field of the ferroelectric second material either induces a deficiency of charge carriers in the superconductive first material, the superconductive first material being in an under-doped state relative to the same material in the absence of the ferroelectric second material, or an excess of charge carriers in the superconductive first material, the superconductive first material then being in an over-doped state relative to the same superconductive material in the absence of ferroelectric second material. Doping a superconductive material allows the critical temperature of the superconductive first material to be shifted, the critical temperature of the superconductive first material being the temperature below which the resistance of the superconductive first material is negligible.
The document by Crassous et al. reports a device making it possible, on the one hand, to visualize, using an atomic force microscope (AFM), the polarization direction of the ferroelectric second material after an electrical voltage has been applied between the cantilever and the superconductive first material, the cantilever being a conductive atomic scale tip of the AFM allowing, in this case, a voltage to be applied to the surface of the first material. The resistance of the superconductive film is obtained by measuring the voltage produced by the passage of a current of known value.
The device proposed by the publication of Crassous et al. comprises a hybrid structure, taking the form of a small strip, containing a first layer of superconductive material comprising YBaCu3O7, denoted YBCO, and a second layer of ferroelectric material comprising BiFeO3, denoted BFO. The BFO, which is a ferroelectric material known for its high remnance, allows “non-volatile” doping of the superconductive first material of the hybrid structure to be achieved. In the present case, the ferroelectric second material has a perovskite structure and is formed, using conditions known to those skilled in the art, in such a way as to allow an accumulation of charge in an amount ranging up to about 100 μC·cm−2 to be obtained in the (111) direction.
The expression “non-volatile structure” is understood to mean a structure that preserves its properties after application of the electrical voltage has been stopped. In other words, the polarization direction of the ferroelectric second layer remains unchanged after application of the electrical voltage has been stopped. Therefore, the doping state of the superconductive first material remains unchanged after application of the electrical voltage has been stopped.
FIGS. 1a and 1b show a hybrid structure according to the prior art.
FIG. 1a shows the hybrid structure 1 comprising a stack of a superconductive first material 2 and a ferroelectric second material 3 at rest. In other words, no voltage is applied between the cantilever 4 of the AFM and the first layer of superconductive material 2. The polarization of the second layer of ferroelectric material 3 is uniform.
In this case, the polarization of the second layer of ferroelectric material 3 is oriented toward the first layer of superconductive material 2, in other words “downward”. The orientation of the polarization of the ferroelectric second material 3 is represented by arrows oriented from top to bottom. According to the measurements published by Crassous et al., if a voltage of −4.5 V is applied between the cantilever 4 of the AFM and the first layer of superconductive material 2, the polarization direction of the second layer of ferroelectric material 3 remains unchanged, the polarization of the second material 3 remaining uniform and oriented from top to bottom. Continuously increasing the voltage applied up to a value below 3 V does not modify the orientation of the polarization, the latter remaining uniform over the entirety of the second layer of ferroelectric material 3.
FIG. 1b shows the hybrid structure 1; an electrical voltage is applied between the cantilever 4 of the AFM and the first layer of superconductive material 2, the applied voltage being 3 V or more. The orientation of the polarization of the second layer of material 3 is locally inverted. The local inversion of polarization is represented by an arrow oriented from bottom to top located beneath the cantilever 4 of the AFM. The polarization direction is locally oriented from bottom to top, generating locally an excess of charge carriers in the superconductive first material 2 enabling its over-doping. The local polarization of the second layer of material 3 will remain in this new state oriented from bottom to top even if the electrical voltage between the cantilever 4 of the AFM and the first layer of superconductive material 2 drops to zero.
The polarization direction of the second layer of ferroelectric material 3 may once more be locally inverted by applying a voltage lower than −3 V between the cantilever 4 of the AFM and the first layer of superconductive material 2.
FIGS. 1a and 1b clearly show a change of polarization direction obtained for a DC electrical voltage value higher in absolute value than a threshold electrical voltage value Us—in the present case the threshold electrical voltage Us is equal to 3 V.
FIG. 2 shows the hysteresis cycle of the ferroelectric second material 3 containing BFO.
This graphical representation was produced using a hybrid structure 1 such as described above. This figure again demonstrates the existence of a threshold electrical voltage Us above which, in absolute value, the orientation of the polarization of the ferroelectric second material 3 is inverted. This threshold voltage value Us allows an electric field of strength at least equal to the strength of the inverting electric field Er to be generated. The expression “inverting electric field” is understood to mean the field allowing the orientation of the polarization of the ferroelectric second material 3 to be inverted in the direction parallel to the direction of the stack.
FIG. 3 shows the resistance of a hybrid structure 1 such as described above as a function of temperature and as a function of the doping state of the first layer of superconductive material 2.
To determine the resistance values, an electrical current density of 1.7 kA·cm−2 was made to flow through the hybrid structure 1.
First measurements of the electrical voltage as a function of temperature across the terminals of a first zone corresponding to the under-doped state of the superconductive first material 2, and second measurements of the voltage across the terminals of a second zone corresponding to the over-doped state of the superconductive first material 2, were carried out. The resistances as a function of temperature were then deduced from the voltage measurements carried out for the over-doped state and the under-doped state of the first layer of superconductive material 2.
A first curve (the solid line) corresponds to the resistance variation determined for the first superconductive material 2 in the under-doped state as a function of temperature.
In a first temperature range comprised between 0 K and 14 K, the resistance of the superconductive first material 2 is almost zero. In a second temperature range comprised between 14 K and 150 K, the resistance of the superconductive first material 2 substantially increases with temperature. In the under-doped state the superconductive first material 2 thus has a first critical temperature Tc1, the first critical temperature Tc1 being equal to 14 K. Below this first critical temperature Tc1, the resistance of the superconductive first material 2 is negligible.
A second curve (the discontinuous line) corresponds to the resistance variation determined for the superconductive first material 2 in the over-doped state as a function of temperature.
In a third temperature range comprised between 0 and 37 K, the resistance of the superconductive first material 2 is almost zero. In a fourth temperature range comprised between 37 K and 150 K, the resistance substantially increases with temperature. In the doped state, a second critical temperature Tc2 of the superconductive first material 2 is equal to 37 K, below this temperature the resistance of the superconductive first material 2 is negligible.
The curves representing the variation in the resistance of a hybrid structure 1 as a function of temperature for a superconductive first material 2 in the doped state and undoped state are of similar shape. The second critical temperature Tc2, corresponding to the over-doped state of the first superconductive material 2, is above the first critical temperature Tc1, corresponding to the under-doped state of the superconductive first material 2. This difference in the critical temperature of the over-doped state and of the under-doped state of the superconductive first material 2 allows a first temperature interval ΔT1 to be defined in which the difference in the resistance of the over-doped state and of the under-doped state of the superconductive first material 1 is nonzero for a given operating temperature. In the present case, this temperature interval is comprised between 14 K and at least 150 K. The temperature of 150 K was the highest for which measurements were taken in the experiments shown in FIG. 3. However, a nonzero difference in resistance is achieved for any temperature above the first critical temperature Tc1. The largest difference in resistance is observed in the temperature interval comprised between Tc1 and Tc2.
Therefore, changing the state of the superconductive first material 2 in the temperature interval above 14K allows the resistance of the hybrid structure 1 to be altered.
FIG. 4 shows a first application of a hybrid structure 1 according to the prior art.
The hybrid structure 1 comprises the stack of the first layer of superconductive material 2, the second layer of the ferroelectric material 3 and an upper electrode or gate comprising a conductive material 5. A DC electrical voltage is applied between the conductive electrode 5 and the superconductive first material 2. Applying a positive or negative voltage makes it possible to achieve, under the upper gate, a local nonvolatile change in the polarization direction of the second layer of ferroelectric material 3, the change in the polarization direction being reversible by simply applying an electrical voltage of opposite value. The change in polarization direction engenders a change in the state of the superconductive first material 2, which will then pass from an under-doped state to an over-doped state, or vice versa. For a given operating temperature comprised in the first temperature interval ΔT1, the change of state of the superconductive first material 2 from an under-doped state to an over-doped state induces a decrease in the resistance of the superconductive material. In contrast, changing the state of the superconductive first material 2 from an over-doped state to an under-doped state induces an increase in the resistance of the superconductive first material 2.
This device allows, in a “switching” mode, one resistance value to be switched to another. By optimizing the choice of the operating temperature, this device allows, in the “switching” mode, current to flow or be blocked. The device proposed in the prior art does not allow the resistance to be gradually varied.